I checked out the Coco Hotel Copenhagen (formerly Copenhagen Crown Hotel) close to the central station. It looks like an attractive property at Vesterbrogade 41.
I would also look into the Carlton 66 Hotel which is a part of the Guldsmeden chain. It is closer to the center of town than the Bertrams (now closed). Other hotels getting great press include The Admiral Hotel on the harbor in a 200-year-old converted warehouse, the Hotel SP34 a boutique design hotel and the Hotel D’Angleterra.